A function is an operation that assigns to each number in a domain, a unique number in a codomain. The function is usually given in the form of an equation,for example, Each value of gives a unique value of if this were not so, we would not have a function. To sketch a function we need to find a set of points. This is most easily done by drawing up a table.
3 
2 
1 
0 
1 
2 
3 

9 
4 
1 
0 
1 
4 
9 

+1 
1 
1 
1 
1 
1 
1 
1 
10 
5 
2 
1 
2 
5 
10 
If we have a graph of a function and we want to know the domain and codomain, then we can find them by looking at the axes. To find the domain, we look at the xaxis. To find the range or codomain we look at theaxis. For the function above, the function is restricted tovalues in the rang [3,3] so the domain is the interval, [3,3] and the codomain or range is the interval [1,10].
The graph below,has domain(notice the vertical dotted line, indicating that atsocan not be equal to 1) and codomainIf the graph tends toward anorvalue without reaching it, then that value cannot be in the domain or codomain respectively.